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 Skip Navigation LinksMath Help > Number Theory > Theorems > Kronecker Symbol

Kronecker symbol

Kronecker symbol —  ( a

n
)  , where a and n are any integers, is an extension of the Jacobi symbol,

by adding the following rules:

( a

2
)  = ( 2

a
)  for odd a, and  ( a

2
)  = 0 for even a
( a

-1
)  =  {

-1 if a<0,
1 if a≥0 

( a

0
)  =  {

1 if a=±1,
0 otherwise

 

Internet references

Mathworld: Kronecker Symbol

Wikipedia: Kronecker symbol

Related pages in this website

Euler's Criterion — a way to tell if a number is a quadratic residue (mod p)

Legendre symbol —  ( a

p
)  , where a is any integer, and p is an odd prime
Jacobi symbol —  ( a

n
)  , where a is any integer, and n is a positive integer greater than 2, an extension of the Legendre symbol.

 

 


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